Question

How do you simplify `(-5+6i)/(5+4i)`?

Answer 1

`(-1+50i)/41`

Explanation:

The automatic response is to try change the denominator such that it is no longer of type Complex. We do this by using what is called its 'Conjugate'. That is: `5-4i`.

To do this we multiply the whole by the value of 1 but in the form of

`(5-4i)/(5-4i)` so that we do not effectively change the value of the whole.
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`(-5+6i)/(5+4i) xx (5-4i)/(5-4i)`

`(-25+20i+30i-24i^2)/(25-20i+20i-16i^2)`

But `i^2=-1` giving:

`(-1+50i)/41`